A siege is what happens when a group of people surround another group of people and stop them from escaping, or getting food and water. Without supplies, those inside will have to surrender at some point. There were many sieges in Medieval times, normally at a castle or town. Sieges took a long time, perhaps months, but were almost always successful, unless another group of people came to rescue those inside, by fighting the besiegers.
Well known sieges were: